Integrated optical filters having elliptic transfer functions are proposed using two-dimensional arrays of synchronously tuned mutually coupled microring resonators. Analysis of microring filter topologies of the most general form is facilitated by the formulation of an energy-coupling matrix for the microring array. A method for synthesizing elliptic microring filter transfer functions having the prescribed transmission poles and zeros is also presented. The approach involves representing the microring filter by an equivalent electrical network of coupled LC oscillators and applying the coupling matrix technique developed for micro-wave filters to determine the coupling parameters. An example of a sixth-order elliptic function filter is presented to demonstrate the feasibility of using mutually coupled microring resonators to realize optical filters having finite transmission zeros in the transfer function.
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